After jumping, this cliff diver undergoes effective free fall. Cliff diving is a sport in which athletes twist and flip on their way down. Even with the air resistance, these divers will accelerate the whole way down.

### Uniform Acceleration

Acceleration that does not change in time is called **uniform or constant acceleration.** The velocity at the beginning of the time interval is called initial velocity, \begin{align*}v_i\end{align*}, and the velocity at the end of the time interval is called final velocity, \begin{align*}v_f\end{align*}. In a velocity versus time graph for uniform acceleration, the slope of the line is the acceleration. The equation that describes the curve is **\begin{align*}v_f = v_i + at\end{align*}**.

**Example 1**

If an automobile with a velocity of 4.0 m/s accelerates at a rate of 4.0 m/s^{2} for 2.5 s, what is the final velocity?

\begin{align*}v_f = v_i + at = 4.0 \ \text{m/s} + (4.0 \ \text{m/s}^2)(2.5 \ \text{s}) = 4.0 \ \text{m/s} + 10. \ \text{m/s} = 14 \ \text{m/s}\end{align*}

**Example 2**

If a cart slows from 22.0 m/s with an acceleration of -2.0 m/s^{2}, how long does it require to get to 4 m/s?

**\begin{align*}t=\frac{v_f-v_i}{a}=\frac{-18 \ \text{m/s}}{-2.0 \ \text{m/s}^2}=9.0 \ \text{s}\end{align*}**

### Interactive Simulation

### Summary

- Acceleration that does not change in time is uniform, or constant, acceleration.
- The equation relating initial velocity, final velocity, time, and acceleration is \begin{align*}v_f = v_i + at\end{align*}.

### Review

- If an object has zero acceleration, does that mean it has zero velocity? Give an example.
- If an object has zero velocity, does that mean it has zero acceleration? Give an example.
- If the acceleration of a motorboat is 4.0 m/s
^{2}, and the motorboat starts from rest, what is its velocity after 6.0 s? - The friction of the water on a boat produces an acceleration of -10. m/s
^{2}. If the boat is traveling at 30. m/s and the motor is shut off, how long it take the boat to slow down to 5.0 m/s?